University of Michigan Council, Center for Education

Although widespread agreement exists that content knowledge is essential for effective instruction, what is actually meant by "content knowledge" varies. Terms such as "mathematical knowledge" and "pedagogical content knowledge" are used in different ways by different people, often without anyone noticing the confusion. We suggest that efforts to design opportunities for teachers to learn mathematics are hampered by this lack of specification and discrimination, and the lack of shared definitions for terms and ideas about "content knowledge." In this session, we will explore a set of distinctions that our research group has developed to "map" the territory of "mathematical knowledge for teaching" and consider what might be involved in helping teachers learn these different domains of content knowledge.

----Deborah Loewenberg Ball and Hyman Bass

Hyman Bass is the Roger Lyndon Collegiate Professor of mathematics and mathematics education at the University of Michigan. His mathematical research publications cover broad areas of algebra, with connections to geometry, topology and number theory. Bass is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. Bass chaired the Mathematical Sciences Education Board at the NRC, and the Committee on Education of the American Mathematical Society, and he is President of the International Commission on Mathematics Instruction. During the past eight years he has been collaborating with Deborah Ball and her research group at the University of Michigan on the mathematical knowledge and resources entailed in the teaching of mathematics at the elementary level. In all of this work, a major challenge has been to build bridges between diverse professional communities and stakeholders involved in mathematics education, both here and abroad.